Research Information System
Modeling Earth Systems and Environment, vol.11, no.2, 2025 (ESCI, Scopus)
The spread of infectious diseases remains a significant threat to global health and stability. A crucial aspect of controlling and mitigating the impact of these diseases is a thorough understanding of their dynamics. This study thoroughly examines a discrete-time epidemic model’s stability and bifurcation characteristics, considering both vaccination and vital dynamics. From studying the stability of fixed points, we have derived the conditions for how the system responds to parameter changes and the circumstances needed for profound disease control. Additionally, our investigation of the bifurcation occurrences provides a clearer picture of the relationship between small parameter changes and qualitative changes in system behaviour. Our study of a one-parametric bifurcation and a codimension two-parameter bifurcation mainly illustrates the complex interactions between various parameters and their effects on the system’s dynamics. We also show how crucial chaos control is in modelling epidemics, and we apply the hybrid control method to control the chaos in the model. Managing chaos in the system is essential for preventing the spread of infectious diseases and ensuring long-term disease control. Our numerical simulations support our findings.